Overview

Student course taking patterns at a large university are complicated and driven by a number of underlying factors. The declared major of a student tends to determine their basic course requirements, and the mathematics progression will follow the ultimate course need for that major. In turn, the ultimate course will fall into a number of typical groups that can be summarized as

Major Groups and Goal Mathematics Courses

Group

Course Goal

STEM Intending - Science

MAC 2311/2281 Calculus I (C1)

STEM Intending - Engineering

MAC 2312/2282 Calculus II (C2)

STEM Intending - Mathematics or Computational Focus

MAC 2313/2283 Calculus III (C3) or higher

Business Related

MAC 1105 College Algebra (CA) or MAC 2233 Business Calculus (BC)

Health Science

MAC 1105 College Algebra (CA), MAC 1147 Precalculus (PC), or MAC 2311 Calculus (C1)

Non-STEM Intending

MGF 1106 Social Choice Math (SM) or MGF 1107 Finite Math (FM)

Here we analyze the course flows for the STEM Intending, Health Science and Business Related groups. These students typically enter college at either the College Algebra (CA), Precalculus (PC) or Calculus I (C1) levels and progress to some level that is dependent on their specific major.

In an effort to understand some aspects of student course taking behavior, we collected data from the institutional records for students taking College Algebra (CA) MAC 1105, Precalculus College Algebra (PCA) MAC 1140, Precalculus with Trigonometry (PC) MAC 1147, MAC 1114 (TR) Trigonometry, Business Calculus (MAC 2233), Calculus I (C1, including both MAC 2311 Calculus I and MAC 2281 Engineering Calculus I), Calculus II (C2, including both MAC 2312 Calculus II and MAC 2282 Engineering Calculus II), and Calculus III (C3, including both MAC 2313 Calculus III and MAC 2283 Engineering Calculus III). Over the ten year period from Fall 2013 to Summer 2024 we observe 143172 instances of course taking (possibly with repetition) within these courses among students from Fall 2013 to Summer 2024. This total corresponds to 71654 distinct students enrolling over this time period. Subgrouping by course and then splitting the groups into two five-year time periods from Fall 2013 to Summer 2018 and Fall 2018 to Summer 2024, inclusive, the enrollments are as shown in the following table.

Enrollment by Course

Fall 2013 to Summer 2018

Fall 2018 to Summer 2024

Course

#

# Succeed

% Succeed

#

# Succeed

% Succeed

Social Choice Math

7,128

4,528

63.5

3,465

2,445

70.6

Finite Math

5,906

4,047

68.5

5,104

4,052

79.4

College Algebra (1105)

10,248

6,730

65.7

18,504

12,335

66.7

Precalculus College Algebra (1140)

12,418

6,366

51.3

1,267

782

61.7

Precalculus with Trig (1147)

3,220

1,887

58.6

9,817

7,045

71.8

Trigonometry (1114)

6,925

3,575

51.6

1,286

849

66.0

Business Calculus

5,926

3,356

56.6

8,844

6,687

75.6

Eng Calculus 1

820

614

74.9

Eng Calculus 2

1,362

971

71.3

Eng Calculus 3

845

681

80.6

Calculus 1

9,560

5,298

55.4

10,124

7,200

71.1

Calculus 2

6,691

3,703

55.3

6,325

4,509

71.3

Calculus 3

4,045

2,490

61.6

3,342

2,326

69.6

Total

72,067

41,980

58.3

71,105

50,496

71.0

Using this data, we then collected the unique student instances in each course (without repetition), and combined them by student to create the course taking pattern of the student. In what follows, we give the number of students in each course followed by the number of those students who took the next course from CA to C3. We computed two statistics from this process.

First, we calculuated the percentage of students from a given source course (such as CA) found in a given target course (such as C1). This number is computed as

\[\begin{equation*} \frac{\#(\text{students who passed the source course (A/B/C) and attempted the target course})}{\#(\text{students who took the source course})} \end{equation*}\]

We then computed the percentage of students in the target course that came from the source course. This number is computed as

\[\begin{equation*} \frac{\#(\text{students who passed the source course (A/B/C) and attempted the target course})}{\#(\text{students who took the target course})} \end{equation*}\]

Note that in general, the second number is larger than the first since the denominator is smaller.

Visualizing Flow Through

From Fall 2013 to 2018 we can visualize the course taking patterns of unique student instances as shown below.

The plot data is summarized below in the following table.

Source and Target Enrollment by Course - Fall 2013 to Summer 2018

Source

PCA 1140

TR 1114

PC 1147

#

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

1105

8319

1612

19.4

31.5

3300

39.7

36.5

1181

14.2

44.8

1114

5113

2238

43.8

24.8

151

3

5.7

1140

9042

202

2.2

7.7

Total in Target Course

5113

9042

2634

Source and Target Enrollment by Course - Fall 2013 to Summer 2018

Source

BC

C1

C2

C3

#

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

1105

8319

1771

21.3

40.8

1444

17.4

21.1

631

7.6

13.4

271

3.3

9.7

1114

5113

163

3.2

3.8

1949

38.1

28.5

938

18.3

19.9

461

9

16.5

1140

9042

2472

27.3

56.9

2160

23.9

31.6

976

10.8

20.7

466

5.2

16.6

1147

2634

126

4.8

2.9

1352

51.3

19.8

652

24.8

13.8

261

9.9

9.3

2233

4341

120

2.8

1.8

46

1.1

1

22

0.5

0.8

2311

6844

2846

41.6

60.2

1320

19.3

47.1

2312

4724

1889

40

67.4

Total in Target Course

4341

6844

4724

2802

Similarly, the data from Fall 2018 to Summer 2024 is shown below.

and the data for this collected in the following tables.

Source and Target Enrollment by Course - Fall 2018 to Summer 2024

Source

PCA 1140

TR 1114

PC 1147

#

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

1105

15358

238

1.5

22

298

1.9

29.5

4018

26.2

47.5

1114

1084

259

23.9

25.7

41

3.8

0.5

1140

1009

56

5.6

0.7

Total in Target Course

1084

1009

8451

Source and Target Enrollment by Course - Fall 2018 to Summer 2024

Source

BC

C1

C2

C3

#

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

1105

15358

2891

18.8

37.2

1864

12.1

20.8

751

4.9

12

288

1.9

8.6

1114

1084

18

1.7

0.2

295

27.2

3.3

105

9.7

1.7

41

3.8

1.2

1140

1009

40

4

0.5

227

22.5

2.5

75

7.4

1.2

28

2.8

0.8

1147

8451

195

2.3

2.5

3597

42.6

40.1

1329

15.7

21.2

481

5.7

14.4

2233

7766

144

1.9

1.6

44

0.6

0.7

19

0.2

0.6

2311

8981

3460

38.5

55.2

1156

12.9

34.5

2312

6268

2131

34

63.6

Total in Target Course

7766

8981

6268

3351

Course Flows Allowing for Multiple Attempts

We can also compile the data allowing for student repetition of courses. That is, we aggregate the attempts for a source course counting each attempt made by a student, and then consider whether or not that student attempts a target course some number of times and count each instance there as well.

From the Fall of 2018 to Summer 2024 is shown below.

and the data for this collected in the following tables.

Source and Target Enrollment by Course All Instances- Fall 2018 to Summer 2024

Source

PCA 1140

TR 1114

PC 1147

#

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

1105

10327

1879

18.2

28

3829

37.1

31.4

1400

13.6

44.2

1114

6700

2886

43.1

23.6

209

3.1

6.6

1140

12211

287

2.4

9.1

Total in Target Course

6700

12211

3169

Source and Target Enrollment by Course All Instances- Fall 2018 to Summer 2024

Source

BC

C1

C2

C3

#

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

1105

10327

2081

20.2

35.4

1616

15.6

17

703

6.8

10.6

297

2.9

7.5

1114

6700

200

3

3.4

2499

37.3

26.4

1143

17.1

17.2

564

8.4

14.2

1140

12211

3306

27.1

56.3

2689

22

28.4

1181

9.7

17.7

558

4.6

14

1147

3169

159

5

2.7

1592

50.2

16.8

747

23.6

11.2

299

9.4

7.5

2233

5871

147

2.5

1.6

50

0.9

0.8

24

0.4

0.6

2311

9481

3701

39

55.6

1711

18

43.1

2312

6656

2659

39.9

66.9

Total in Target Course

5871

9481

6656

3974

From the Fall of 2018 to Summer 2024 is shown below.

and the data for this collected in the following tables.

Source and Target Enrollment by Course All Instances- Fall 2018 to Summer 2024

Source

PCA 1140

TR 1114

PC 1147

#

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

1105

18375

264

1.4

22

347

1.9

31.3

4419

24

44.8

1114

1201

303

25.2

27.3

43

3.6

0.4

1140

1109

62

5.6

0.6

Total in Target Course

1201

1109

9859

Source and Target Enrollment by Course All Instances- Fall 2018 to Summer 2024

Source

BC

C1

C2

C3

#

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

#

% from Src

% of Tgt

1105

18375

3203

17.4

36.6

1968

10.7

18.4

780

4.2

10.4

293

1.6

7.2

1114

1201

20

1.7

0.2

328

27.3

3.1

114

9.5

1.5

43

3.6

1.1

1140

1109

41

3.7

0.5

240

21.6

2.2

77

6.9

1

30

2.7

0.7

1147

9859

215

2.2

2.5

3982

40.4

37.3

1418

14.4

18.9

503

5.1

12.4

2233

8762

152

1.7

1.4

44

0.5

0.6

19

0.2

0.5

2311

10686

3796

35.5

50.6

1249

11.7

30.8

2312

7497

2486

33.2

61.2

Total in Target Course

8762

10686

7497

4059